A catalyst is disposed on an exhaust passage of an internal combustion engine so as to purify exhaust. Regarding such a catalyst, Patent Literature 1 points out the problem of the possibility of occurrence of a crack on a catalyst support due to an increase in difference in temperature between a side wall surface of the support of an electric heating catalyst and the vicinity of a side wall during acceleration immediately after cold starting of an internal combustion engine. In view of this, a device disclosed in Patent Literature 1 is designed to transit the air-fuel ratio of exhaust toward a rich side during acceleration immediately after cold starting so as to reduce energy of the exhaust in order to suppress an increase in difference in temperature.